Du finner liknende eksempler i videosnutten Integrasjon av konstant funksjon:

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Regn ut

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$\\displaystyle{\\int \\var{a} dx}$ = [[0]]

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$\\displaystyle{\\int \\var{a+2} dt}$ = [[1]]

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Regn ut

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$\\displaystyle{\\int \\simplify{x^{n} }dx}$ = [[0]]

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$\\displaystyle{\\int \\simplify{t^{a} }dt}$ = [[1]]

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Du finner noen liknende eksempler i videoen Integrasjon av potenser

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Du finner et liknende eksempel i videoen Integrasjon og derivasjon

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Regn ut

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$\\displaystyle{\\int \\left(\\simplify{{a}x^3+{b}x^2+{c}x+{d} }\\right)dx} =$ [[0]]

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Her bruker vi at

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$\\displaystyle{\\int \\frac{1}{x}dx =\\simplify{ln(abs(x))+C}}$

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Du finner et eksempel i videosnutten Integrasjon av uttrykk som inneholder 1/x:

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", "unitTests": []}], "type": "gapfill", "prompt": "

Finn det ubestemte integralet

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$\\displaystyle{\\int \\left(\\simplify{{a}x^{n}+{c}/x}\\right)dx}$ = [[0]]

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NB: for å skrive inn $\\simplify{abs(x)}$, kan du taste \"abs(x)\" (uten hermetegn)

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Du finner et lignende eksempel i videosnutten Integrasjon av eksponentialfunksjoner

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", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true}], "prompt": "

Regn ut det ubestemte integralet

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$\\displaystyle{\\int \\left(\\simplify{{a}exp({n}t)+{b}exp(-{m}t)}\\right)dt}=$ [[0]]

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Her kan vi starte med å skrive om uttrykket:

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$\\displaystyle{\\int \\simplify{(e^({m+1}x)-{c})/e^({m+1}x)}dx= \\int \\left(\\simplify{e^({m+1}x)/e^({m+1}x)-{c}/e^({m+1}x)}\\right)dx = \\int \\left(\\simplify{1-{c}e^(-{m+1}x)}\\right)dx}$

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Deretter kan vi integrere ledd for ledd, på samme måte som i forrige oppgave.

", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true}], "prompt": "

Regn ut det ubestemte integralet

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$\\displaystyle{\\int \\simplify{(e^({m+1}x)-{c})/e^({m+1}x)}dx}=$ [[0]]

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Finn det ubestemte integralet

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$\\displaystyle{\\int \\left(\\simplify{x^{n}+{b}^x}\\right)}dx =$ [[0]]

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Her kan vi bruke at $\\displaystyle{\\int a^x dx = \\frac{1}{\\ln a}a^x+C}$.

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Et lignende eksempel:

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$\\displaystyle{\\int (3x^2-10^x)dx = 3\\cdot \\frac{1}{3}x^3-\\frac{1}{\\ln 10}10^x+C = x^3 -\\frac{10^x}{\\ln 10} +C}$

Husk at

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$\\displaystyle{\\int \\sin(x) dx = -\\cos(x)+C}$

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$\\displaystyle{\\int \\cos(x) dx = \\sin(x)+C}$

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", "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "unitTests": [], "sortAnswers": false, "stepsPenalty": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "

Finn det ubestemte integralet

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$\\displaystyle{\\int \\left(\\simplify{{a}sin(x)+{b}cos(x)}\\right) dx}=$ [[0]]

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Du finner et lignende eksempel i videoen Trigonometrisk funksjon med lineær kjerne

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", "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "unitTests": [], "sortAnswers": false, "stepsPenalty": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "

Finn det ubestemte integralet

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$\\displaystyle{\\int \\simplify{{a}cos(pi/{n}x-pi)}dx}=$ [[0]]

"}], "rulesets": {}, "type": "question"}, {"name": "Line\u00e6r nevner", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "metadata": {"description": "", "licence": "None specified"}, "variables": {"b": {"description": "", "definition": "random(-5..5 except [0,a, -a])", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}, "a": {"description": "", "definition": "random(2..5)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}}, "advice": "", "ungrouped_variables": ["a", "b"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "tags": [], "variable_groups": [], "statement": "", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "gapfill", "showCorrectAnswer": true, "gaps": [{"type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "unitTests": [], "checkVariableNames": false, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "marks": 1, "showFeedbackIcon": true, "showPreview": true, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "answerSimplification": "all, !Noleadingminus", "vsetRange": [0, 1], "failureRate": 1, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "answer": "1/{a}ln(abs({a}x+{b}))+C"}], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "steps": [{"type": "information", "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Du finner et lignende eksempel i videoen Brøk med lineær nevner:

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", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": []}], "prompt": "

Finn det ubestemte integralet

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$\\displaystyle{\\int \\simplify{1/({a}x+{b})} dx}=$ [[0]]

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